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of 67
pro vyhledávání: '"de Laat, David"'
We prove that the $D_4$ root system (the set of vertices of the regular $24$-cell) is the unique optimal kissing configuration in $\mathbb R^4$, and is an optimal spherical code. For this, we use semidefinite programming to compute an exact optimal s
Externí odkaz:
http://arxiv.org/abs/2404.18794
We show that the spectral embeddings of all known triangle-free strongly regular graphs are optimal spherical codes (the new cases are $56$ points in $20$ dimensions, $50$ points in $21$ dimensions, and $77$ points in $21$ dimensions), as are certain
Externí odkaz:
http://arxiv.org/abs/2403.16874
We give universal bounds on the fraction of nontrivial zeros having given multiplicity for L-functions attached to a cuspidal automorphic representation of $\mathrm{GL}_m/\mathbb{Q}$. For this, we apply the higher-level correlation asymptotic of Hejh
Externí odkaz:
http://arxiv.org/abs/2303.01095
We compute the second and third levels of the Lasserre hierarchy for the spherical finite distance problem. A connection is used between invariants in representations of the orthogonal group and representations of the general linear group, which allo
Externí odkaz:
http://arxiv.org/abs/2211.16471
We define three-point bounds for sphere packing that refine the linear programming bound, and we compute these bounds numerically using semidefinite programming by choosing a truncation radius for the three-point function. As a result, we obtain new
Externí odkaz:
http://arxiv.org/abs/2206.15373
Autor:
Leijenhorst, Nando, de Laat, David
We study a primal-dual interior point method specialized to clustered low-rank semidefinite programs requiring high precision numerics, which arise from certain multivariate polynomial (matrix) programs through sums-of-squares characterizations and s
Externí odkaz:
http://arxiv.org/abs/2202.12077
Publikováno v:
J. High Energ. Phys. 12 (2020) 66
We carry out a numerical study of the spinless modular bootstrap for conformal field theories with current algebra $U(1)^c \times U(1)^c$, or equivalently the linear programming bound for sphere packing in $2c$ dimensions. We give a more detailed pic
Externí odkaz:
http://arxiv.org/abs/2006.02560
Assuming the generalized Riemann hypothesis, we give asymptotic bounds on the size of intervals that contain primes from a given arithmetic progression using the approach developed by Carneiro, Milinovich and Soundararajan [Comment. Math. Helv. 94, n
Externí odkaz:
http://arxiv.org/abs/2005.02393
In this paper we give an algorithm to round the floating point output of a semidefinite programming solver to a solution over the rationals or a quadratic extension of the rationals. We apply this to get sharp bounds for packing problems, and we use
Externí odkaz:
http://arxiv.org/abs/2001.00256
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